Introduction to Mathematical Oncology

Chapter 4

Physiologically Structured Tumor Growth

4.1 Introduction

In this chapter we further explore the hypothesis explaining Gompertz-like tumor growth kinetics proposed by Gyllenberg and Webb. They extended their original quiescence model (section 2.4) to a more sophisticated framework that increases the realism beyond what simple models from Chapter 2 can handle. This new framework also introduces an important modeling feature—physiological stage structure (see [9] for an introduction to such models; detailed theory can be found in [4, 5]). These models, like the MCS models of Chapter 3, are based on partial differential equations.

Recall that Gyllenberg and Webb’s original model (2.64, section 2.4) assumes that, besides being proliferative ...